arXiv subjects

Anshid Aboobacker

Publications and source records attributed to Anshid Aboobacker.

3 recordsLinked to original sources

arXiv2026

$k$-type Chaos for Induced Group Actions on Hyperspaces

This paper investigates the correlation between $k$-type dynamical properties of $\mathbb{Z}^d$-actions on compact metric spaces and their induced actions on the corresponding hyperspaces. We extend the classical results from discrete dynamical systems and general group actions to the specific setting of $k$-type dynamics. Specifically, we define and study $k$-type transitivity, $k$-type mixing, $k$-type weak mixing, and $k$-type Li-Yorke chaos for induced hyperspace actions, establishing that these properties transfer from the base system to the hyperspace under appropriate conditions.

math.DS↗

arXiv2025

$k$-type entropy of $\mathbb{Z}^d$ actions

We introduce the concept of $k$-type entropy for dynamical systems generated by $\mathbb{Z}^d$-actions on compact metric spaces. We investigate its fundamental properties and establish connections with classical entropy and other $k$-type dynamical notions. The $k$-type entropy of some $\mathbb{Z}^2$-actions on a two dimensional torus is also calculated.

math.DS↗

arXiv2025

$k$-type chaos of $\mathbb{Z}^d$ actions

In this paper, we define and study the notions of $k$-type proximal pairs, $k$-type asymptotic pairs and $k$-type Li Yorke sensitivity for dynamical systems given by $\mathbb{Z}^d$ actions on compact metric spaces. We prove the Auslander-Yorke dichotomy theorem for $k$-type notions. The preservation of some of these notions under uniform conjugacy is also studied. We also study relations between these notions and their analogous notions in the usual dynamical systems.

math.DS↗